Through Hannah Arendt's New Yorker coverage of his trial in 1961 and her book Eichmann in Jerusalem, Adolf Eichmann is remembered mostly for her famous catchphrase, "the banality of evil". It was a persuasive if erroneous reading. There was very little banal about Eichmann, though at his trial most expressed disappointment at his insignificance. Where was the strutting SS officer in his death's-head cap who had boasted of killing millions of Jews? Only Harold Rosenberg, writing in Commentary, noted a level of calculation in his performance, "created over the years for just this courtroom situation".

Eichmann's trial was taken to be about many things; for most it was about totalitarianism. Only Eichmann saw it as being about himself. Indeed, his own convoluted version, with him as death's reluctant travel agent, is now taken to be more accurate than the prosecution's case of grand conspirator. This is not to excuse him. In this excellent and thorough biography, with its emphasis on the political mechanisms and confusions that allowed for such a moral collapse, Cesarani points out that, by the time he was finished in Hungary in 1944, "he was rotten from the inside out". He explains Eichmann less in the context of totalitarianism than by charting the process through which a man not hard-wired to kill ends up a willing collaborator in the business of genocide.

The result is scrupulously objective in a way its subject would have approved. Any hatchet-job is reserved for Arendt, dismissed as an unreliable witness because her prejudices ironically mirrored those of Eichmann. Her German Jewish bourgeois background expressed itself in a long-nurtured contempt for the "Ostjuden" and her comments on the Israelis veered into racism. It is an instructive lesson, verging on black comedy, on the complications of prejudice.

As much as Eichmann's, the prejudice of others determined the deportation of Europe's Jews. Hungarian officials proved especially willing subscribers, undertaking all duties from asset stripping to loading the trains, leaving Eichmann with little to do. He played the violin at soirees in a quartet of co-workers. Young women in his office found him handsome and "cheery". He played table tennis with the secretaries. In his book Danube, Claudio Magris noted: "The technocrat of massacre loved meditation, inner absorption, the peace of the woods, maybe even prayer."

His undoing was the deep humourlessness noted by his captors, accompanied by an even more striking inflexibility of mind. His lethal delusion was exemplified on the one hand by his insistence on himself as a referent, carrying out orders approved by his superiors; and on the other by his disappointment when a book he wrote in May 1942, with an anticipated print run of 50,000, was banned. Its subject was statistical data of Jewish transports. Of his work, he commented without irony: "Time just flew by."

Cesarani dispels myths of Eichmann's unhappy childhood, placing him against the normal but selective background of Austrian Calvinism - very different from the previous picture of an embittered man who turned Nazi on grounds of social disgrace and economic hardship or out of resentment against Jewish employers. Eichmann, diligent worker and dutiful son, grew up in a milieu where dislike of Jews was unremarkable; where little animosity was displayed towards individual Jews but "Jewry" was viewed as an alien body in the German national organism. It was a fantasy to which he became increasingly susceptible, but he was not driven in the first instance by racial hatred.

His was a job-in-waiting rather than one envisioned, with no sign that the underfunded SS department he joined before the war would become instrumental in anti-Jewish policy. Cesarani takes the current position on the Third Reich as more muddle than efficiency. At his trial Eichmann described in numbing detail administrative structures of such byzantine complexity and density that he vanished into insignificance within them, until one of the judges, moved to exasperation, declared: "It is clear to us that, in German, the predicate comes at the end of the sentence, but it takes too long to reach the predicate." His captors had previously noted his German as "hideous - the jargon of a Nazi bureaucrat pronounced in a mixture of Berlin and Austrian accents and further garbled by his liking for endlessly complicated sentences in which he himself would occasionally get lost".

The road to genocide was neither as predictable nor predetermined as has been assumed. Eichmann's department distanced itself from Goebbels's rabble-rousing with cooler arguments, declaring that Jews were entitled to their own national homeland and Germany should do all it could to assist. Eichmann first showed his teeth in 1938 in Austria, speeding up Jewish emigration and devising a funding mechanism whereby the wealthy paid for the emigration of the poor, a blatant scam that made sense only in the context of discrimination and terror.

His more acceptable face was evident the following year. As emigration still remained the order of the day, he was happy to cooperate with Zionist smugglers organising illicit transports of Jews to Palestine. But his essential indifference became apparent in the enforced deportation of Jews to Poland in 1939, a project dressed up in the language of "resettlement" that left thousands to rot in an inhospitable landscape. The lesson learned by Eichmann's superiors from his lethal efficiency was that it was possible with little expenditure of effort or capital to deport wholesale. Eichmann then went to work on the Poles. His development was complete before extermination became official. The job remained the same regardless of the fate of his transportations.

The notorious Wannsee conference of 1942 here becomes less of a point of no return and more of a rationalisation of an existing unofficial policy. Mass shootings of civilian populations on the eastern front had already been carried out and local pogroms were encouraged. By the end of 1941, more than half a million Jews had been slaughtered and the killing had grown indiscriminate. And no one wanted the responsibility of being lumbered with Eichmann's deportations.

Eichmann's own transition to genocide was not entirely smooth. He had been revolted observing killings in the field and recorded his loss of face at Auschwitz where "they laughed, naturally, when my nerves broke down and I couldn't keep my military dignity". He moaned that annihilation wasn't a political solution, being enough of a careerist to know that previous solutions offered more chance of prestige and promotion than mass murder.

After the war he demonstrated a cunning for survival noted at his trial. Life in hiding in Germany consisted of several rural idylls, apparently untroubled by conscience, but after his escape to South America the career took on an air of willed failure. He missed out on the Nazi gravy train in Argentina. Josef Mengele, Auschwitz's "angel of death", was moving in exalted circles. Eichmann, by contrast, was on the verge of squalor. The two men met and failed to get on. Mengele made an offer of free medical treatment, which Eichmann, perhaps mindful of the doctor's wartime experiments, declined. All his businesses failed. He even had a go at his old job, working as transportation manager (for a firm manufacturing sanitary ware), but that didn't work out either.

His capture was not the zealous affair his kidnapping suggests. No one cared particularly about Eichmann. The world was moving on. A Mossad agent on the case said it was left to a blind man living 10 hours away from Buenos Aires to prove Eichmann's identity. By then he was so down on his luck no one could believe a high-ranking Nazi fugitive could reside in so nondescript a place. Confronted by such a poor wretch his captors were "touched, even a bit disgusted" by his shabby underwear. In a way, the only person who cared by then about him was Eichmann himself.

He was a willing captive, recognising that without trial he was nothing. His arraignment in Israel was the justification of a ponderous man eager to state his case, and the one unshakeable element in his defence was a capacity for self-justification. The element missing in Cesarani's compelling portrait is Eichmann the actor, the theatrical man who liked the uniform and the power it bestowed. In that one sees the historical destiny described by Primo Levi, who wrote of a man "ringed by death", surrounded by and selected by death just as the millions he had dispatched were selected for death. He joined them, willing but unrepentant, on May 31 1962, hanged in a makeshift execution cell.